7
Chemical
7-1 Lewis Dot Formulas of Atoms Ionic Bonding
7-2 Formation of Ionic Compounds Covalent Bonding
7-3 Formation of Covalent Bonds 7-4 Lewis Formulas for Molecules
and Polyatomic Ions 7-5 The Octet Rule
7-6 Resonance
7-7 Limitations of the Octet Rule for Lewis Formulas
7-8 Polar and Nonpolar Covalent Bonds
7-9 Dipole Moments
7-10 The Continuous Range of Bonding Types
OBJECTIVES
After you have studied this chapter, you should be able to • Write Lewis dot representations of atoms
• Predict whether bonding between specified elements will be primarily ionic, covalent, or polar covalent
• Compare and contrast characteristics of ionic and covalent compounds • Describe how the properties of compounds depend on their bonding • Describe how the elements bond by electron transfer (ionic bonding) • Describe energy relationships in ionic compounds
• Predict the formulas of ionic compounds
• Describe how elements bond by sharing electrons (covalent bonding) • Write Lewis dot and dash formulas for molecules and polyatomic ions • Recognize exceptions to the octet rule
• Write formal charges for atoms in covalent structures
• Describe resonance, and know when to write resonance structures and how to do so
• Relate the nature of bonding to electronegativity differences
Carbon atoms are covalently bonded together in a three-dimensional array to make diamond, the hardest substance known.
C
C
hemical bonding refers to the attractive forces that hold atoms together in compounds. There are two major classes of bonding. (1) Ionic bonding results from electrostatic interactions among ions, which often results from the net transfer of one or more electrons from one atom or group of atoms to another. (2) Cova-lent bonding results from sharing one or more electron pairs between two atoms. These two classes represent two extremes; all bonds between atoms of different elements have at least some degree of both ionic and covalent character. Compounds containing predom-inantly ionic bonding are called ionic compounds. Those that are held together mainly by covalent bonds are called covalent compounds. Some nonmetallic elements, such as H2, Cl2, N2, and P4, also involve covalent bonding. Some properties usually associated with many simple ionic and covalent compounds are summarized in the following list. The differences in these properties can be accounted for by the differences in bonding between the atoms or ions.Ionic CompoundsCovalent Compounds 1. They are solids with high melting 1. They are gases, liquids, or solids with
2. points (typically400°C). 2. low melting points (typically300°C). 2. Many are soluble in polar solvents 2. Many are insoluble in polar solvents.
2. such as water.
3. Most are insoluble in nonpolar 3. Most are soluble in nonpolar solvents,
2. solvents, such as hexane, C6H14, and 2. such as hexane, C6H14, and carbon
2. carbon tetrachloride, CCl4. 2. tetrachloride, CCl4.
4. Molten compounds conduct 4. Liquid and molten compounds do not
2. electricity well because they contain 2. conduct electricity.
2. mobile charged particles (ions).
5. Aqueous solutions conduct electricity 5. Aqueous solutions are usually poor
2. well because they contain mobile 2. conductors of electricity because most
2. charged particles (ions). 2. do not contain charged particles. 6. They are often formed between two 6. They are often formed between two
2. elements with quite different 2. elements with similar
electronega-2. electronegativities, usually a metal 2. tivities, usually nonmetals.
2. and a nonmetal. 2.
LEWIS DOT FORMULAS OF ATOMS
The number and arrangements of electrons in the outermost shells of atoms determine the chemical and physical properties of the elements as well as the kinds of chemical bonds they form. We write Lewis dot formulas (or Lewis dot representations, or just Lewis formulas) as a convenient bookkeeping method for keeping track of these “chemically important electrons.” We now introduce this method for atoms of elements; in our discus-sion of chemical bonding in subsequent sections, we will frequently use such formulas for atoms, molecules, and ions.
7-1
As you study Chapters 7 and 8, keep in mind the periodic similarities that you learned in Chapters 4 and 6. What you learn about the bonding of an element usually applies to the other elements in the same column of the periodic table, with minor variations.
7-1 Lewis Dot Formulas of Atoms 271
As we saw in Section 4-2, aqueous solutions of some covalent compounds do conduct electricity, because they react with water to some extent to form ions.
The distinction between polar and nonpolar molecules is made in Section 7-8.
Chemical bonding usually involves only the outermost electrons of atoms, also called valence electrons. In Lewis dot representations, only the electrons in the outermost occu-pied s and p orbitals are shown as dots. Paired and unpaired electrons are also indicated. Table 7-1 shows Lewis dot formulas for the representative elements. All elements in a given group have the same outer-shell electron configuration. It is somewhat arbitrary on which side of the atom symbol we write the electron dots. We do, however, represent an electron pair as a pair of dots and an unpaired electron as a single dot.
IONIC BONDING
FORMATION OF IONIC COMPOUNDS
The first kind of chemical bonding we shall describe is ionic bonding. We recall (Section 2-3) that an ion is an atom or a group of atoms that carries an electrical charge. An ion in which the atom or group of atoms has fewer electrons than protons is positively charged, and is called a cation; one that has more electrons than protons is negatively charged, and is called an anion. An ion that consists of only one atom is described as a monatomic ion. Examples include the chloride ion, Cl, and the magnesium ion, Mg2. An ion that contains more than one atom is called a polyatomic ion. Examples include the ammo-nium ion, NH4; the hydroxide ion, OH; and the sulfate ion, SO42. The atoms of a polyatomic ion are held together by covalent bonds. In this section we shall discuss how ions can be formed from individual atoms; polyatomic ions will be discussed along with other covalently bonded species.
Ionic bonding is the attraction of oppositely charged ions (cations and anions) in large numbers to form a solid. Such a solid compound is called an ionic solid.
7-2
The chemical and physical properties of an ion are quite different from those of the atom from which the ion is derived. For example, an atom of Na and an Naion are quite different.
Group Number of electrons in valence shell IA H Li Na K Rb Cs Fr 1 IIA Be Mg Ca Sr Ba Ra 2 IIIA B Al Ga In Tl 3 Period 7 Period 6 Period 5 Period 4 Period 3 Period 2 Period 1 IVA 4 C Si Ge Sn Pb VA 5 N P As Sb Bi VIA 6 O S Se Te Po F Cl Br I At VIIA 7 VIIIA 8 (except He) He Ne Ar Kr Xe Rn For the Group A elements, the
number of valence electrons (dots in the Lewis formula) for the neutral atom is equal to the group number. Exceptions: H (one valence electron) and He (two valence electrons).
For example, Al has the electron configuration [Ar] 3s23p1. The three dots in the Lewis dot formula for Al represent the two s electrons (the pair of dots) and the p electron (the single dot) beyond the noble gas configuration. Because of the large numbers of dots, such formulas are not as useful for the transition and inner transition elements.
As our previous discussions of ionization energy, electronegativity, and electron affinity would suggest, ionic bonding can occur easily when elements that have low ionization energies (metals) react with elements having high electronegativities and very negative electron affinities (nonmetals). Many metals are easily oxidized — that is, they lose elec-trons to form cations; and many nonmetals are readily reduced — that is, they gain elecelec-trons to form anions.
When the electronegativity difference, (EN), between two elements is large, as between a metal and a nonmetal, the elements are likely to form a compound by ionic bonding (transfer of electrons).
Let us describe some combinations of metals with nonmetals to form ionic compounds.
Group IA Metals and Group VIIA Nonmetals
Consider the reaction of sodium (a Group IA metal) with chlorine (a Group VIIA nonmetal). Sodium is a soft silvery metal (mp 98°C), and chlorine is a yellowish-green corrosive gas at room temperature. Both sodium and chlorine react with water, sodium vigorously. By contrast, sodium chloride is a white solid (mp 801°C) that dissolves in water with no reaction and with the absorption of just a little heat. We can represent the reac-tion for its formareac-tion as
2Na(s) Cl2(g) 88n 2NaCl(s) sodium chlorine sodium chloride
We can understand this reaction better by showing electron configurations for all species. We represent chlorine as individual atoms rather than molecules, for simplicity.
11Na [Ne] __h Na [Ne] 1e lost
3s
88n
17Cl [Ne] __hg __hg __hg __h Cl [Ne] __hg __hg __hg __hg 1egained
3s 3p 3s 3p
Freshly cut sodium has a metallic luster. A little while after being cut, the sodium metal surface turns white as it reacts with the air.
7-2 Formation of Ionic Compounds273
Some ionic compounds. Clockwise from front right: sodium chloride (NaCl, white); copper(II) sulfate pentahydrate (CuSO45H2O, blue); nickel(II) chloride hexahydrate (NiCl26H2O, green); potassium dichromate (K2Cr2O7, orange); and cobalt(II) chloride hexahydrate (CoCl26H2O, red). One mole of each substance is shown.
In this reaction, Na atoms lose one electron each to form Naions, which contain only ten electrons, the same number as the preceding noble gas, neon. We say that sodium ions have the neon electronic structure: Nais isoelectronic with Ne (Section 6-5). In contrast, Cl atoms gain one electron each to form Cl ions, which contain 18 electrons. This is the same number as the following noble gas, argon; Cl is isoelectronic with Ar. These processes can be represented compactly as
Na 88n Na e and Cl e 88n Cl
Similar observations apply to most ionic compounds formed by reactions between repre-sentative metals and reprerepre-sentative nonmetals.
We can use Lewis dot formulas (Section 7-1) to represent the reaction.
The formula for sodium chloride is NaCl because the compound contains Na and Clin a 1:1 ratio. This is the formula we predict based on the fact that each Na atom contains only one electron in its outermost occupied shell and each Cl atom needs only one electron to fill completely its outermost p orbitals.
The chemical formula NaCl does not explicitly indicate the ionic nature of the compound, only the ratio of ions. Furthermore, values of electronegativities are not always available. So we must learn to recognize, from positions of elements in the periodic table and known trends in electronegativity, when the difference in electronegativity is large enough to favor ionic bonding.
The farther apart across the periodic table two Group A elements are, the more ionic their bonding will be.
The greatest difference in electronegativity occurs from the lower left to upper right, so CsF ([EN] 3.2) is more ionic than LiI ([EN] 1.5).
All the Group IA metals (Li, Na, K, Rb, Cs) will react with the Group VIIA elements (F, Cl, Br, I) to form ionic compounds of the same general formula, MX. All the resulting ions, Mand X, have noble gas configurations. Once we understand the bonding of one member of a group (column) in the periodic table, we know a great deal about the others in the family. Combining each of the five common alkali metals with each of the four common halogens gives 5 4 20 possible compounds. The discussion of NaCl presented here applies also to the other 19 such compounds.
The collection of isolated positive and negative ions occurs at a higher energy than the elements from which they are formed. The ion formation alone is not sufficient to account for the formation of ionic compounds. Some other favorable factor must account for the observed stability of these compounds. Because of the opposite charges on Naand Cl, an attractive force is developed. According to Coulomb’s Law, the force of attraction, F, between two oppositely charged particles of charge magnitudes q and q is directly proportional to the product of the charges and inversely proportional to the square of the distance separating their centers, d. Thus, the greater the charges on the ions and the smaller the ions are, the stronger the resulting ionic bonding. Of course, like-charged ions repel each other, so the distances separating the ions in ionic solids are those at which the attractions exceed the repulsions by the greatest amount.
The energy associated with the attraction of separated gaseous positive and negative ions to form an ionic solid is the crystal lattice energy of the solid. For NaCl, this energy
Cl
Na Na[ Cl ]
The loss of electrons is oxidation (Section 4-5). Na atoms are oxidized to form Naions.
The gain of electrons is reduction (Section 4-5). Cl atoms are reduced to form Clions.
Formulas for some of these are
LiF NaF KF LiCl NaCl KCl LiBr NaBr KBr LiI NaI KI Coulomb’s Law is F q d q 2 . The symbol means “is proportional to.” The noble gases are excluded from this generalization.
is 789 kJ/mol; that is, one mole of NaCl solid is 789 kJ lower in energy (more stable) than one mole of isolated Naions and one mole of isolated Clions. We could also say that it would require 789 kJ of energy to separate one mole of NaCl solid into isolated gaseous ions. The stability of ionic compounds is thus due to the interplay of the energy cost of ion formation and the energy repaid by the crystal lattice energy. The best trade-off usually comes when the monatomic ions of representative elements have noble gas configurations.
The structure of common table salt, sodium chloride (NaCl), is shown in Figure 7-1. Like other simple ionic compounds, NaCl(s) exists in a regular, extended array of posi-tive and negaposi-tive ions, Naand Cl. Distinct molecules of solid ionic substances do not exist, so we must refer to formula units (Section 2-3) instead of molecules. The forces that hold all the particles together in an ionic solid are quite strong. This explains why such substances have quite high melting and boiling points (a topic that we will discuss more fully in Chapter 13). When an ionic compound is melted or dissolved in water, its charged particles are free to move in an electric field, so such a liquid shows high electrical conduc-tivity (Section 4-2, part 1).
We can represent the general reaction of the IA metals with the VIIA elements as follows:
2M(s) X2 88n 2MX(s) M Li, Na, K, Rb, Cs; X F, Cl, Br, I The Lewis dot representation for the generalized reaction is
Group IA Metals and Group VIA Nonmetals
Next, consider the reaction of lithium (Group IA) with oxygen (Group VIA) to form lithium oxide, a solid ionic compound (mp 1700°C) (see next page). We may represent the reaction as
4Li(s) O2(g) 88n 2Li2O(s) lithium oxygen lithium oxide
The formula for lithium oxide, Li2O, indicates that two atoms of lithium combine with one atom of oxygen. If we examine the structures of the atoms before reaction, we can see the reason for this ratio.
3Li __hg __h Li __hg __ 1 e lost 1s 2s 1s 2s 3Li __hg __h N 88n Li __hg __ 1 e lost 1s 2s 1s 2s 8O __hg __hg __hg __h __h O2 __hg __hg __hg __hg __hg 2 egained 1s 2s 2p 1s 2s 3p In a compact representation, 2[Li 88n Lie] and O2e 88n O2 The Lewis dot formulas for the atoms and ions are
Lithium ions, Li, are isoelectronic with helium atoms (2 e). Oxide ions, O2, are isoelec-tronic with neon atoms (10 e).
O
2Li O 2Li[ ]2
X X
2M X 2 (M[ ])
Figure 7-1 A representation of the crystal structure of NaCl. Each Cl ion (green) is surrounded by six sodium ions, and each Naion (gray) is surrounded by six chloride ions. Any NaCl crystal includes billions of ions in the pattern shown. Adjacent ions actually are
in contact with one another; in this drawing, the structure has been expanded to show the spatial arrangement of ions. The lines do not represent covalent bonds. Compare with Figure 2-7, a space-filling drawing of the NaCl structure. 7-2 Formation of Ionic Compounds275
Na Cl
Although the oxides of the other Group IA metals are prepared by different methods, similar descriptions apply to compounds between the Group IA metals (Li, Na, K, Rb, Cs) and the Group VIA nonmetals (O, S, Se, Te, Po).
Each Li atom has 1 ein its valence shell, one more ethan a noble gas configuration, [He]. Each O atom has 6 ein its valence shell and needs 2 emore to attain a noble gas configuration [Ne]. The Liions are formed by oxidation of Li atoms, and the O2ions are formed by reduction of O atoms.
Isoelectronic species have the same
number of electrons (see Section 6-5). Some isoelectronic species:
O2 8 protons 10 electrons F 9 protons 10 electrons Ne 10 protons 10 electrons Na 11 protons 10 electrons Mg2 12 protons 10 electrons
The very small size of the Liion gives it a much higher charge density (ratio of charge to size) than that of the larger Naion (Figure 6-1). Similarly, the O2ion is smaller than the Clion, so its smaller size and double negative charge give it a much higher charge density. These more concentrated charges and smaller sizes bring the Liand O2 ions closer together in Li2O than the Naand Clions are in NaCl. Consequently, the qqproduct in the numerator of Coulomb’s Law is greater in Li2O, and the d2term in the denominator is smaller. The net result is that the ionic bonding is much stronger (the lattice energy is much more negative) in Li2O than in NaCl. This is consistent with the higher melting temperature of Li2O (1700°C) compared to NaCl (801°C).
Group IIA Metals and Group VIA Nonmetals
As our final illustration of ionic bonding, consider the reaction of calcium (Group IIA) with oxygen (Group VIA). This reaction forms calcium oxide, a white solid ionic compound with a very high melting point, 2580°C.
2Ca(s) O2(g) 88n 2CaO(s) calcium oxygen calcium oxide
Again, we show the electronic structure of the atoms and ions, representing the inner elec-trons by the symbol of the preceding noble gas.
20Ca [Ar] __hg Ca2 [Ar] __ 2 elost
4s 4s
88n
8O [He] __hg __hg __h __h O2 [He] __hg __hg __hg __hg 2 egained
2s 2p 2s 2p
The Lewis dot notation for the reacting atoms and the resulting ions is
Calcium ions, Ca2, are isoelectronic with argon (18 e), the preceding noble gas. Oxide ions, O2, are isoelectronic with neon (10 e), the following noble gas.
Ca2is about the same size as Na(see Figure 6-1) but carries twice the charge, so its charge density is higher. Because the attraction between the two small, highly charged ions Ca2and O2is quite high, the ionic bonding is very strong, accounting for the very high melting point of CaO, 2580°C.
Binary Ionic Compounds: A Summary
Table 7-2 summarizes the general formulas of binary ionic compounds formed by the representative elements. “M” represents metals, and “X” represents nonmetals from the indicated groups. In these examples of ionic bonding, each of the metal atoms has lost one, two, or three electrons, and each of the nonmetal atoms has gained one, two, or three electrons. Simple (monatomic) ions rarely have charges greater than 3 or 3. Ions with greater charges would interact so strongly with the electron clouds of other ions that the electron clouds would be very distorted, and considerable covalent character in the bonds would result. Distinct molecules of solid ionic substances do not exist. The sum of the attractive forces of all the interactions in an ionic solid is substantial. Therefore, binary ionic compounds have high melting and boiling points.
The d- and f-transition elements form many compounds that are essentially ionic in character. Many simple ions of transition metals do not have noble gas configurations.
O
Ca O Ca2[ ]2
Lithium is a metal, as the shiny surface of freshly cut Li shows. Where it has been exposed to air, the surface is covered with lithium oxide. This discussion also applies to other
ionic compounds between any Group IIA metal (Be, Mg, Ca, Sr, Ba) and any Group VIA nonmetal (O, S, Se, Te).
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Screen 8.8, Electron Configurations in Ions.
The distortion of the electron cloud of an anion by a small, highly charged cation is called polarization. Binary compounds contain two elements.
TABLE 7-2 Simple Binary Ionic Compounds
General Ions
Metal Nonmetal Formula Present Example mp (°C)
IA* VIIA 88n MX (M, X) LiBr 547
IIA VIIA 88n MX2 (M2, 2X) MgCl2 708
IIIA VIIA 88n MX3 (M3, 3X) GaF3 800 (subl)
IA*† VIA 88n M
2X (2M, X2) Li2O 1700
IIA VIA 88n MX (M2, X2) CaO 2580
IIA VIA 88n M2X3 (2M3, 3X2) Al2O3 2045
IA* VA 88n M3X (3M, X3) Li3N 840
IIA VA 88n M3X2 (3M2, 2X3) Ca3P2 ⬇1600
IIIA VA 88n MX (M3, X3) AlP
*Hydrogen is a nonmetal. All binary compounds of hydrogen are covalent, except for certain metal hydrides such as NaH and CaH2, which contain hydride, H, ions.
†As we saw in Section 6-8, the metals in Groups IA and IIA also commonly form peroxides (containing the O
22ion) or
superox-ides (containing the O2ion). See Table 6-4. The peroxide and superoxide ions contain atoms that are covalently bonded to one another.
Introduction to Energy Relationships in Ionic Bonding
The following discussion may help you to understand why ionic bonding occurs between elements with low ionization energies and those with high electronegativities. There is a general tendency in nature to achieve stability. One way to do this is by lowering potential energy; lower energies generally represent more stable arrangements.
Let us use energy relationships to describe why the ionic solid NaCl is more stable than a mixture of individual Na and Cl atoms. Consider a gaseous mixture of one mole of sodium atoms and one mole of chlorine atoms, Na(g) Cl(g). The energy change associated with the loss of one mole of electrons by one mole of Na atoms to form one mole of Naions (step 1 in Figure 7-2) is given by the first ionization energy of Na (see Section 6-3).
Na(g) 88n Na(g) e first ionization energy 496 kJ/mol
This is a positive value, so the mixture Na(g) e Cl(g) is 496 kJ/mol higher in energy than the original mixture of atoms (the mixture Na e Cl is less stable than the mixture of atoms).
The energy change for the gain of one mole of electrons by one mole of Cl atoms to form one mole of Clions (step 2) is given by the electron affinity of Cl (see Section 6-4).
Cl(g) e 88n Cl(g) electron affinity 349 kJ/mol
This negative value, 349 kJ/mol, lowers the energy of the mixture, but the mixture of separated ions, Na Cl, is still higher in energy (less stable) by (496 349) kJ/mol 147 kJ/mol than the original mixture of atoms (the red arrow in Figure 7-2). Thus, just the formation of ions does not explain why the process occurs. The strong attractive force between ions of opposite charge draws the ions together into the regular array shown in Figure 7-1. The energy associated with this attraction (step 3) is the crystal lattice energy of NaCl, 789 kJ/mol.
Na(g) Cl(g) 88n NaCl(s) crystal lattice energy 789 kJ/mol
The crystal (solid) formation thus further lowers the energy to (147 789) kJ/mol 642 kJ/mol. The overall result is that one mole of NaCl(s) is 642 kJ/mol lower in energy
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COVALENT BONDING
Ionic bonding cannot result from a reaction between two nonmetals, because their elec-tronegativity difference is not great enough for electron transfer to take place. Instead, reactions between two nonmetals result in covalent bonding.
A covalent bond is formed when two atoms share one or more pairs of electrons. Covalent bonding occurs when the electronegativity difference, (EN), between elements (atoms) is zero or relatively small.
Figure 7-2 A schematic
representation of the energy changes that accompany the process
Na(g) Cl(g) n NaCl(s).
The red arrow represents the positive energy change (unfavorable) for the process of ion formation,
Na(g) Cl(g) n Na(g) Cl(g). The blue arrow represents the negative energy change (favorable) for the overall process, including the formation of the ionic solid.
(more stable) than the original mixture of atoms (the blue arrow in Figure 7-2). Thus, we see that a major driving force for the formation of ionic compounds is the large electro-static stabilization due to the attraction of the ionic charges (step 3).
In this discussion we have not taken into account the fact that sodium is a solid metal or that chlorine actually exists as diatomic molecules. The additional energy changes involved when these are changed to gaseous Na and Cl atoms, respectively, are small enough that the overall energy change starting from Na(s) and Cl2(g) is still negative.
Na(g) e Cl(g)
Na(g) Cl(g)
Increasing potential energy (less stable)
Na(g) Cl(g) EA of Cl 349 kJ/mol
Net energy change for Na(g) Cl(g) Na(g) Cl(g)
147 kJ/mol
Net energy change for 642 kJ/molCl(g) Na(g) NaCl(s) 1st IE of Na 496 kJ/mol Crystal lattice energy of NaCl 789 kJ/mol NaCl(s) 1 2 3 (Enrichment, continued)
In predominantly covalent compounds the bonds between atoms within a molecule (intramolecular bonds) are relatively strong, but the forces of attraction between molecules (intermolecular forces) are relatively weak. As a result, covalent compounds have lower melting and boiling points than ionic compounds. The relation of bonding types to phys-ical properties of liquids and solids will be developed more fully in Chapter 13.
FORMATION OF COVALENT BONDS
Let us look at the simplest case of covalent bonding, the reaction of two hydrogen atoms to form the diatomic molecule H2. As you recall, an isolated hydrogen atom has the ground state electron configuration 1s1, with the probability density for this one electron spher-ically distributed about the hydrogen nucleus (Figure 7-3a). As two hydrogen atoms approach each other, the electron of each hydrogen atom is attracted by the nucleus of the other hydrogen atom as well as by its own nucleus (Figure 7-3b). If these two elec-trons have opposite spins so that they can occupy the same region (orbital), both elecelec-trons can now preferentially occupy the region between the two nuclei (Figure 7-3c), because they are attracted by both nuclei. The electrons are shared between the two hydrogen atoms, and a single covalent bond is formed. We say that the 1s orbitals overlap so that both electrons are now in the orbitals of both hydrogen atoms. The closer together the atoms come, the more nearly this is true. In that sense, each hydrogen atom then has the helium configuration 1s2.
The bonded atoms are at lower energy (more stable) than the separated atoms. This is shown in the plot of energy versus distance in Figure 7-4. As the two atoms get closer together, however, the two nuclei, being positively charged, exert an increasing repulsion on each other. At some distance, a minimum energy, 435 kJ/mol, is reached; it corre-sponds to the most stable arrangement and occurs at 0.74 Å, the actual distance between two hydrogen nuclei in an H2molecule. At greater internuclear separation, the repulsive forces diminish, but the attractive forces decrease even faster. At smaller separations, repul-sive forces increase more rapidly than attractive forces. The magnitude of this stabilization
7-3
Figure 7-3 A representation of the formation of a covalent bond between two hydrogen atoms. The position of each positively charged nucleus is represented by a black dot. Electron density is indicated by the depth of shading. (a) Two hydrogen atoms separated by a large distance. (b) As the atoms approach each other, the electron of each atom is attracted by the positively charged nucleus of the other atom, so the electron density begins to shift. (c) The two electrons can both occupy the region where the two 1s orbitals overlap; the electron density is highest in the region between the nuclei of the two atoms.
7-3 Formation of Covalent Bonds279
Figure 7-4 The potential energy of the H2molecule as a function of the distance between the two nuclei. The lowest point in the curve, 435 kJ/mol, corresponds to the internuclear distance actually observed in the H2molecule, 0.74 Å. (The minimum potential energy, 435 kJ/mol, corresponds to the value of 7.23 1019joule per H
2molecule.) Energy is compared with that of two separated hydrogen atoms.
H H H H H2 (a) (b) (c)
Increasing internuclear distance
H H H H H H Increasing ener gy 0 H2 molecule 0.74 Å – 435molkJ
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Screen 9.3, Chemical Bond Formation: Covalent Bonding, and Screen 10.3, Valence Bond Theory.
is called the HXH bond energy. Bond energies for covalent bonds will be discussed more extensively in Section 15-9.
Other pairs of nonmetal atoms share electron pairs to form covalent bonds. The result of this sharing is that each atom attains a more stable electron configuration — frequently the same as that of the nearest noble gas. This results in a more stable arrangement for the bonded atoms. (This is discussed in Section 7-5.) Most covalent bonds involve sharing of two, four, or six electrons — that is, one, two, or three pairs of electrons. Two atoms form a single covalent bond when they share one pair of electrons, a double covalent bond when they share two electron pairs, and a triple covalent bond when they share three electron pairs. These are usually called simply single, double, and triple bonds. Covalent bonds that involve sharing of one and three electrons are known, but are relatively rare. In a Lewis formula, we represent a covalent bond by writing each shared electron pair either as a pair of two dots between the two atom symbols or as a dash connecting them. Thus, the formation of H2from H atoms could be represented as
HT TH 88n HSH or HXH
where the dash represents a single bond. Similarly, the combination of two fluorine atoms to form a molecule of fluorine, F2, can be shown as
The formation of a hydrogen fluoride, HF, molecule from a hydrogen atom and a fluo-rine atom can be shown as
We will see many more examples of this representation.
In our discussion, we have postulated that bonds form by the overlap of two atomic orbitals. This is the essence of the valence bond theory, which we will describe in more detail in the next chapter. Another theory, molecular orbital theory, is discussed in Chapter 9. For now, let us concentrate on the number of electron pairs shared and defer the discussion of which orbitals are involved in the sharing until the next chapter.
LEWIS FORMULAS FOR MOLECULES AND POLYATOMIC IONS
In Sections 7-1 and 7-2 we drew Lewis formulas for atoms and monatomic ions. In Section 7-3, we used Lewis formulas to show the valence electrons in three simple molecules. A water molecule can be represented by either of the following diagrams.
In dash formulas, a shared pair of electrons is indicated by a dash. There are two double bonds in carbon dioxide, and its Lewis formula is
The covalent bonds in a polyatomic ion can be represented in the same way. The Lewis formula for the ammonium ion, NH4, shows only eight electrons, even though the N atom has five electrons in its valence shell and each H atom has one, for a total of
C
C O O
O O or
dot formula dash formula O H H O H H or
dot formula dash formula
7-4
F H F H F H or F F F F F F orThe bonding in the other halogens, Cl2, Br2, and I2, is analogous to that in F2.
The bonding in gaseous HCl, HBr, and HI is analogous to that in HF.
An H2O molecule has two shared electron pairs, that is, two single covalent bonds. The O atom also has two unshared pairs.
A CO2molecule has four shared electron pairs in two double bonds. The central atom (C) has no unshared pairs.
In H2O, two of the six valence electrons of an oxygen atom are used in covalent bonding; the one valence electron of each hydrogen atom is used in covalent bonding.
In CO2, the four valence electrons of a carbon atom are used in covalent bonding; two of the six valence electrons of each oxygen atom are used in covalent bonding.
A polyatomic ion is an ion that contains more than one atom.
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Screen 9.4, Lewis Electron Dot Structures.
5 4(1) 9 electrons. The NH4ion, with a charge of 1, has one less electron than the original atoms.
The writing of Lewis formulas is an electron bookkeeping method that is useful as a first approximation to suggest bonding schemes. It is important to remember that Lewis dot formulas only show the number of valence electrons, the number and kinds of bonds, and the order in which the atoms are connected. They are not intended to show the three-dimensional shapes of molecules and polyatomic ions. We will see in Chapter 8, however, that the three-dimensional geometry of a molecule can be predicted from its Lewis formula.
THE OCTET RULE
Representative elements usually attain stable noble gas electron configurations when they share electrons. In the water molecule eight electrons are in the outer shell of the O atom, and it has the neon electron configuration; two electrons are in the valence shell of each H atom, and each has the helium electron configuration. Likewise, the C and O of CO2 and the N of NH3and the NH4ion each have a share in eight electrons in their outer shells. The H atoms in NH3and NH4each share two electrons. Many Lewis formulas are based on the idea that
in most of their compounds, the representative elements achieve noble gas configu-rations.
This statement is usually called the octet rule, because the noble gas configurations have 8 ein their outermost shells (except for He, which has 2 e).
For now, we restrict our discussion to compounds of the representative elements. The octet rule alone does not let us write Lewis formulas. We still must decide how to place the electrons around the bonded atoms — that is, how many of the available valence elec-trons are bonding elecelec-trons (shared) and how many are unshared elecelec-trons (associated with only one atom). A pair of unshared electrons in the same orbital is called a lone pair. A simple mathematical relationship is helpful here:
S N A
S is the total number of electrons shared in the molecule or polyatomic ion. N is the total number of valence shell electrons needed by all the atoms in the molecule or ion to achieve noble gas configurations (N 8 number of atoms that are not H, plus 2 number of H atoms).
A is the number of electrons available in the valence shells of all of the (repre-sentative) atoms. This is equal to the sum of their periodic group numbers. We must adjust A, if necessary, for ionic charges. We add electrons to account for negative charges and subtract electrons to account for positive charges.
7-5
N H H H H N H H H Hdot formula dash formula
The NH3molecule, like the NH4
ion, has eight valence electrons about the N atom.
H
H N H
H
H N H or
7-5 The Octet Rule 281
In some compounds, the central atom does not achieve a noble gas
configuration. Such exceptions to the octet rule are discussed in Section 7-7.
The representative elements are those in the A groups of the periodic table.
Let us see how this relationship applies to some species whose Lewis formulas we have already shown.
For F2,
N 2 8 (for two F atoms) 16 eneeded A 2 7 (for two F atoms) 14 eavailable
S N A 16 14 2 eshared
The Lewis formula for F2shows 14 valence electrons total, with 2 eshared in a single bond.
For HF,
N 1 2 (for one H atom) 1 8 (for one F atom) 10 eneeded A 1 1 (for one H atom) 1 7 (for one F atom) 8 eavailable
S N A 10 8 2 eshared
The Lewis formula for HF shows 8 valence electrons total, with 2 eshared in a single bond.
For H2O,
N 2 2 (for two H atoms) 1 8 (for one O atom) 12 eneeded A 2 1 (for two H atoms) 1 6 (for one O atom) 8 eavailable
S N A 12 8 4 eshared
The Lewis formula for H2O shows 8 valence electrons total, with a total of 4 eshared, 2 ein each single bond.
For CO2,
N 1 8 (for one C atom) 2 8 (for two O atoms) 24 eneeded A 1 4 (for one C atom) 2 6 (for two O atoms) 16 eavailable
S N A 24 16 8 eshared
The Lewis formula for CO2shows 16 valence electrons total, with a total of 8 eshared, 4 ein each double bond.
For NH4,
N 1 8 (for one N atom) 4 2 (for four H atoms) 16 eneeded
A 1 5 (for one N atom) 4 1 (for four H atoms) 1 (for 1 charge) 8 eavailable S N A 16 8 8 eshared
The Lewis formula for NH4shows 8 valence electrons total, with all 8 eshared, 2 e in each single bond.
The following general steps describe the use of the S N A relationship in constructing dot formulas for molecules and polyatomic ions.
Writing Lewis Formulas
1. Select a reasonable (symmetrical) “skeleton” for the molecule or polyatomic ion. a. The least electronegative element is usually the central element, except that H is never the central element, because it forms only one bond. The least
elec-F F F H O H H O C O
The 1 ionic charge is due to a
deficiency of one erelative to the neutral atoms.
H H
H N H
tronegative element is usually the one that needs the most electrons to fill its octet. Example: CS2has the skeleton S C S.
b. Oxygen atoms do not bond to each other except in (1) O2and O3molecules; (2) hydrogen peroxide, H2O2, and its derivatives, the peroxides, which contain the O22group; and (3) the rare superoxides, which contain the O2group. Example: The sulfate ion, SO42, has the skeleton
O O S O
O
c. In ternary oxoacids, hydrogen usually bonds to an O atom, not to the central atom. Example: nitrous acid, HNO2, has the skeleton H O N O. There are a few exceptions to this guideline, such as H3PO3and H3PO2.
d. For ions or molecules that have more than one central atom, the most symmet-rical skeletons possible are used. Examples: C2H4and P2O74have the following skeletons:
H H O O
C C and O P O P O
H H O O
2. Calculate N, the number of valence (outer) shell electrons needed by all atoms in the molecule or ion to achieve noble gas configurations. Examples:
A ternary oxoacid contains three elements — H, O, and another element, often a nonmetal.
7-5 The Octet Rule 283
For H2SO4,
N 2 2 (H atoms) 1 8 (S atom) 4 8 (O atoms) 4 8 32 44 eneeded For ClO4,
N 8 (Cl atoms) 32 (O atoms) 40 eneeded For NO3,
N 1 8 (N atom) 3 8 (O atoms) 32 eneeded
Calculate A, the number of electrons available in the valence (outer) shells of all the atoms. For negatively charged ions, add to this total the number of electrons equal to the charge on the anion; for positively charged ions, subtract the number of elec-trons equal to the charge on the cation. Examples:
For H2SO4,
A 2 1 (H atoms) 1 6 (S atom) 4 6 (O atoms) 2 6 24 32 eavailable For ClO4,
A 1 7 (Cl atom) 4 6 (O atoms) 1 (for 1 charge) 7 24 1 32 eavailable For NO3,
A 1 5 (N atom) 3 6 (O atoms) 1 (for 1 charge) 5 18 1 24 eavailable Calculate S, total number of electrons shared in the molecule or ion, using the
rela-tionship S N A. Examples: 2 4
For the representative elements, the number of valence shell electrons in an atom is equal to its periodic group number. Exceptions: 1 for an H atom and 2 for He.
For compounds containing only representative elements, N is equal to 8 number of atoms that are not H, plus 2 number of H atoms.
For H2SO4,
S N A 44 32
12 electrons shared (6 pairs of eshared) For ClO4,
S N A 40 32
8 electrons shared (4 pairs of eshared) For NO3,
S N A 32 24 8 eshared (4 pairs of eshared) 3. Place the S electrons into the skeleton as shared pairs. Use double and triple bonds
only when necessary. Lewis formulas may be shown as either dot formulas or dash formulas.
Dot Formula Dash Formula (“bonds” in place, (“bonds” in place, Formula Skeleton but incomplete) but incomplete)
H2SO4
ClO4
NO3
4. Place the additional electrons into the skeleton as unshared (lone) pairs to fill the octet of every A group element (except H, which can share only 2 e). Check that the total number of electrons is equal to A, from step 2. Examples:
For H2SO4,
Check: 16 pairs of ehave been used and all octets are satisfied. 2 16 32 e available. For ClO4, O O O O O O O Cl O Cl or O O O O H S H or S O O H H O O O O N O O O N O O O N O O O O Cl O O O O Cl O O O O Cl O S O O H H O O O O O O H S H O O O O H S H
C, N, and O often form double and triple bonds. S can form double bonds with C, N, and O.
Check: 16 pairs of ehave been used and all octets are satisfied. 2 16 32 e available.
For NO3,
Check: 12 pairs of ehave been used and all octets are satisfied. 2 12 24 e available. O O O N O N O O or
C is the central atom, or the element in the middle of the molecule. It needs four more electrons to acquire an octet, and each S atom needs only two more electrons.
7-5 The Octet Rule 285
E
XAMPLE 7-1 Writing Lewis FormulasWrite the Lewis formula for the nitrogen molecule, N2. Plan
We follow the stepwise procedure that was just presented for writing Lewis formulas. Solution
Step 1: The skeleton is N N.
Step 2: N 2 8 16 eneeded (total) by both atoms
Step 2: A 2 5 10 eavailable (total) for both atoms
Step 2: S N A 16 e 10 e 6 eshared Step 3: NSSSN 6 e(3 pairs) are shared; a triple bond.
Step 4: The additional 4 eare accounted for by a lone pair on each N. The complete Lewis formula is
Check: 10 e(5 pairs) have been used.
E
XAMPLE 7-2 Writing Lewis FormulasWrite the Lewis formula for carbon disulfide, CS2, a foul-smelling liquid. Plan
Again, we follow the stepwise procedure to apply the relationship S N A. Solution
Step 1: The skeleton is S C S.
Step 2: N 1 8 (for C) 2 8 (for S) 24 eneeded by all atoms
Step 2: A 1 4 (for C) 2 6 (for S) 16 eavailable
Step 2: S N A 24 e 16 e 8 eshared
Step 3: SSSCSSS 8 e(4 pairs) are shared; two double bonds. N
N or N N
Problem-Solving Tip: Be Careful of the Total Number of Electrons
A very common error in writing Lewis formulas is showing the wrong number of elec-trons. Always make a final check to be sure that the Lewis formula you write shows the same number of electrons you calculated as A.
F
or a slightly different approach than the one used in this text, see the Saunders Interactive GeneralChemistry CD-ROM, Screen 9.5,
Step 4: C already has an octet, so the remaining 8 eare distributed as lone pairs on the S atoms to give each S an octet. The complete Lewis formula is
Check: 16 e(8 pairs) have been used. The bonding picture is similar to that of CO2; this is not surprising, because S is below O in Group VIA.
You should now work Exercise 29.
E
XAMPLE 7-3 Writing Lewis FormulasWrite the Lewis formula for the carbonate ion, CO32. Plan
The same stepwise procedure can be applied to ions. We must remember to adjust A, the total number of electrons, to account for the charge shown on the ion.
Solution
O 2
Step 1: The skeleton is O C O
Step 2: N 1 8 (for C) 3 8 (for O) 8 24 32 eneeded by all atoms
Step 2: A 1 4 (for C) 3 6 (for O) 2 (for the 2 charge)
Step 2: 4 18 2 24 eavailable
Step 2: S N A 32 e 24 e 8 e(4 pairs) shared
O 2
h
Step 3: OSCSSO (Four pairs are shared. At this point it doesn’t matter which O is doubly bonded.)
Step 4: The Lewis formula is
Check: 24 e(12 pairs) have been used. You should now work Exercises 30 and 38.
You should practice writing many Lewis formulas. A few common types of organic compounds and their Lewis formulas are shown here. Each follows the octet rule. Methane, CH4, is the simplest of a huge family of organic compounds called hydrocarbons (composed solely of hydrogen and carbon). Ethane, C2H6, is another hydrocarbon that contains only single bonds. Ethylene, C2H4, has a carbon–carbon double bond, and acetylene, C2H2, contains a carbon–carbon triple bond.
C H H H C H H H H C C H C H H H H ethane, C2H6
methane, CH4 ethylene, C2H4 acetylene, C2H2
C C H H H H O O O O C 2 2 C O O or C C S S S S or
Calcium carbonate, CaCO3, occurs in several forms in nature. The mineral calcite forms very large clear crystals (right); in microcrystalline form it is the main constituent of limestone (top left). Seashells (bottom) are largely calcium carbonate.
Acetylene burns in oxygen with a flame so hot that it is used to weld metals.
For practice, apply the methods of this section to write these Lewis formulas.
Halogen atoms can appear in place of hydrogen atoms in many organic compounds, because hydrogen and halogen atoms each need one more electron to attain noble gas configurations. An example is chloroform, CHCl3. Alcohols contain the group CXOXH; the simplest alcohol is methanol, CH3OH. An organic compound that contains a carbon– oxygen double bond is formaldehyde, H2CO.
H H H CC O H Cl H Cl C Cl O H C H formaldehyde, H2CO methanol, CH3OH chloroform, CHCl3 7-6 Resonance 287 RESONANCE
In addition to the Lewis formula shown in Example 7-3, two other Lewis formulas with the same skeleton for the CO32ion are equally acceptable. In these formulas, the double bond could be between the carbon atom and either of the other two oxygen atoms.
A molecule or polyatomic ion for which two or more Lewis formulas with the same arrangements of atoms can be drawn to describe the bonding is said to exhibit resonance. The three structures above are resonance structures of the carbonate ion. The rela-tionship among them is indicated by the double-headed arrows, mn. This symbol does not mean that the ion flips back and forth among these three structures. The true structure can be described as an average, or hybrid, of the three.
O O C O O 2 O O C O O 2 2 O C
7-6
Problem-Solving Tip: Some Guidelines for Drawing Lewis Formulas
The following guidelines might help you draw Lewis formulas.
1. In most of their covalent compounds, the representative elements follow the octet rule, except that hydrogen always shares only two electrons.
2. Carbon always forms four bonds. This can be accomplished as: a. four single bonds
b. two double bonds
c. two single bonds and one double bond or d. one single bond and one triple bond
3. Hydrogen forms only one bond to another element; thus hydrogen can never be a central atom.
4. In neutral (uncharged) species, nitrogen forms three bonds, and oxygen forms two bonds.
5. Nonmetals can form single, double, or triple bonds, but never quadruple bonds. 6. Carbon forms double or triple bonds to C, N, O, or S atoms; oxygen can form
double bonds with many other elements.
S
ee the Saunders InteractiveGeneral Chemistry CD-ROM,
Screen 9.6, Resonance Structures. C, N, and O often form double and triple bonds. S can form double bonds with C, N, and O.
Experiments show that the CXO bonds in CO32are neither double nor single bonds, but are intermediate in bond length and strength. Based on measurements in many compounds, the typical CXO single bond length is 1.43 Å, and the typical CUO double bond length is 1.22 Å. The CXO bond length for each bond in the CO32ion is inter-mediate at 1.29 Å. Another way to represent this situation is by delocalization of bonding electrons:
The dashed lines include that some of the electrons shared between C and O atoms are delocalized among all four atoms; that is, the four pairs of shared electrons are equally distributed among three CXO bonds.
E
XAMPLE 7-4 Lewis Formulas, ResonanceDraw two resonance structures for the sulfur dioxide molecule, SO2. Plan
The stepwise procedure (Section 7-5) can be used to write each resonance structure. Solution S O q q N 1(8) 2(8) 24 e A 1(6) 2(6) 18 e S N A 6 eshared The resonance structures are
We could show delocalization of electrons as follows:
Remember that Lewis formulas do not necessarily show shapes. SO2molecules are angular, not linear.
You should now work Exercises 50 and 52. S
O O (lone pairs on O not shown) S S O O O O O S O or O S O O 2 O C O
(lone pairs on O atoms not shown) When electrons are shared among
more than two atoms, the electrons are said to be delocalized. The concept of delocalization is important in molecular orbital theory (Chapter 9).
Problem-Solving Tip: Some Guidelines for Resonance Structures
Resonance involves several different acceptable Lewis formulas with the same arrange-ment of atoms. They differ only in the arrangearrange-ments of electron pairs, never in atom positions. The actual structure of such a molecule or ion is the average, or composite, of its resonance structures, but this does not mean that the electrons are moving from one place to another. This average structure is more stable than any of the individual resonance structures.
The rose on the left is in an atmosphere of sulfur dioxide, SO2. Gaseous SO2and its aqueous solutions are used as bleaching agents. A similar process is used to bleach wood pulp before it is converted to paper.
7-6 Resonance 289
Formal Charges
An experimental determination of the structure of a molecule or polyatomic ion is neces-sary to establish unequivocally its correct structure. We often do not have these results available, however. Formal charge is the hypothetical charge on an atom in a molecule or polyatomic ion; to find the formal charge, we count bonding electrons as though they were equally shared between the two bonded atoms. The concept of formal charges helps us to write correct Lewis formulas in most cases. The most energetically favorable formula for a molecule is usually one in which the formal charge on each atom is zero or as near zero as possible.
Consider the reaction of NH3 with hydrogen ion, H, to form the ammonium ion, NH4.
The previously unshared pair of electrons on the N atom in the NH3molecule is shared with the H ion to form the NH4ion, in which the N atom has four covalent bonds. Because N is a Group VA element, we expect it to form three covalent bonds to complete its octet. How can we describe the fact that N has four covalent bonds in species like NH4? The answer is obtained by calculating the formal charge on each atom in NH4 by the following rules:
Rules for Assigning Formal Charges to Atoms of A Group Elements 1. The formal charge, abbreviated FC, on an atom in a Lewis formula is given by
the relationship
FC (group number) [(number of bonds) (number of unshared e)] Formal charges are represented by 䊝 and 䊞 to distinguish them from real charges on ions.
2. In a Lewis formula, an atom that has the same number of bonds as its periodic group number has a formal charge of zero.
3. a. In a molecule, the sum of the formal charges is zero.
b. In a polyatomic ion, the sum of the formal charges is equal to the charge. Let us apply these rules to the ammonia molecule, NH3, and to the ammonium ion, NH4. Because N is a Group VA element, its group number is 5.
In NH3the N atom has 3 bonds and 2 unshared e, and so for N,
FC (group number) [(number of bonds) (number of unshared e)] 5 (3 2) 0 (for N) H H H N H H H N H H H H N H H H N HH
E
n r i c h m e n t
The Hion has a vacant orbital, which accepts a share in the lone pair on nitrogen. The formation of a covalent bond by the sharing of an electron pair that is provided by one atom is called coordinate covalent bond
formation. This type of bond formation
is discussed again in Chapters 10 and 25.
FCs are indicated by 䊝 and 䊞. The sum of the formal charges in a polyatomic ion is equal to the charge on the ion: 1 in NH4.
For H,
FC (group number) [(number of bonds) (number of unshared e)] 1 (1 0) 0 (for H)
The formal charges of N and H are both zero in NH3, so the sum of the formal charges is 0 3(0) 0, consistent with rule 3a.
In NH4the atom has 4 bonds and no unshared e, and so for N,
FC (group number) [(number of bonds) (number of unshared e)] 5 (4 0) 1 (for N)
Calculation of the FC for H atoms gives zero, as shown previously. The sum of the formal charges in NH4is (1) 4(0) 1. This is consistent with rule 3b.
Thus, we see the octet rule is obeyed in both NH3 and NH4. The sum of the formal charges in each case is that predicted by rule 3, even though nitrogen has four covalent bonds in the NH4ion.
This bookkeeping system helps us to choose among various Lewis formulas for a mole-cule or ion, according to the following guidelines.
a. The most likely formula for a molecule or ion is usually one in which the formal charge on each atom is zero or as near zero as possible.
b. Negative formal charges are more likely to occur on the more electronega-tive elements.
c. Lewis formulas in which adjacent atoms have formal charges of the same sign are usually not accurate representations (the adjacent charge rule).
Let us now write some Lewis formulas for, and assign formal charges to, the atoms in nitrosyl chloride, NOCl, a compound often used in organic synthesis. The Cl atom and the O atom are both bonded to the N atom. Two Lewis formulas that satisfy the octet rule are
(i) (ii)
For Cl, FC 7 (2 4) 1 For Cl, FC 7 (1 6) 0 For N, FC 5 (3 2) 0 For N, FC 5 (3 2) 0 For O, FC 6 (1 6) 1 For O, FC 6 (2 4) 0
We believe that (ii) is a preferable Lewis formula, because it has smaller formal charges than (i). We see that a double-bonded terminal Cl atom would have its electrons arranged as /ÅClUX, with the formal charge of Cl equal to 7 (2 4) 1. A positive formal charge on such an electronegative element is quite unlikely, and double bonding to chlorine does not occur. The same reasoning would apply to the other halogens.
N Cl O N Cl O H H H N H
S
ee the Saunders InteractiveGeneral Chemistry CD-ROM,
7-7 Limitations of the Octet Rule for Lewis Formulas 291
LIMITATIONS OF THE OCTET RULE FOR LEWIS FORMULAS
Recall that representative elements achieve noble gas electron configurations in most of their compounds. But when the octet rule is not applicable, the relationship S N A is not valid without modification. The following are general cases for which the proce-dure in Section 7-5 must be modified — that is, there are four types of limitations of the octet rule.
A. Most covalent compounds of beryllium, Be. Because Be contains only two valence shell electrons, it usually forms only two covalent bonds when it bonds to two other atoms. We therefore use four electrons as the number needed by Be in step 2, Section 7-5. In steps 3 and 4 we use only two pairs of electrons for Be.
B. Most covalent compounds of the Group IIIA elements, especially boron, B. The IIIA elements contain only three valence shell electrons, so they often form three covalent bonds when they bond to three other atoms. We therefore use six electrons as the number needed by the IIIA elements in step 2; and in steps 3 and 4 we use only three pairs of electrons for the IIIA elements.
C. Compounds or ions containing an odd number of electrons. Examples are NO, with 11 valence shell electrons, and NO2, with 17 valence shell electrons.
D. Compounds or ions in which the central element needs a share in more than eight valence shell electrons to hold all the available electrons, A. Extra rules are added to steps 2 and 4 of the procedure in Section 7-5 when this is encountered. Step 2a: If S, the number of electrons shared, is less than the number needed to
bond all atoms to the central atom, then S is increased to the number of electrons needed.
Step 4a: If S must be increased in step 2a, then the octets of all the atoms might be satisfied before all of the electrons (A) have been added. Place the extra electrons on the central element.
Many species that violate the octet rule are quite reactive. For instance, compounds containing atoms with only four valence shell electrons (limitation type A above) or six valence shell electrons (limitation type B above) frequently react with other species that supply electron pairs. Compounds such as these that accept a share in a pair of electrons are called Lewis acids; a Lewis base is a species that makes available a share in a pair of elec-trons. (This kind of behavior will be discussed in detail in Section 10-10.) Molecules with an odd number of electrons often dimerize (combine in pairs) to give products that do satisfy the octet rule. Examples are the dimerization of NO to form N2O2(Section 24-15) and NO2to form N2O4(Section 24-15). Examples 7-5 through 7-9 illustrate some limitations and show how such Lewis formulas are constructed.
E
XAMPLE 7-5 Limitations of the Octet RuleWrite the Lewis formula for gaseous beryllium chloride, BeCl2, a covalent compound. Plan
This is an example of limitation type A. So, as we follow the steps in writing the Lewis formula, we must remember to use four electrons as the number needed by Be in step 2. Steps 3 and 4 should show only two pairs of electrons for Be.
7-7
Lewis formulas are not normally written for compounds containing
d- and f-transition metals. The d- and f-transition metals utilize d or f orbitals
(or both) in bonding as well as s and p orbitals. Thus, they can accommodate more than eight valence electrons.
S
ee the Saunders InteractiveGeneral Chemistry CD-ROM,
Screen 9.8, Free Radicals — Exceptions to the Octet Rule.
BF3and BCl3are gases at room temperature. Liquid BBr3and solid BI3are shown here.
Solution
Step 1: The skeleton is Cl Be Cl
see limitation type A g
Step 2: N 2 8 (for Cl) 1 4 (for Be) 20 eneeded
Step 3: A 2 7 (for Cl) 1 2 (for Be) 16 eavailable
Step 3: S N A 20 e 16 e 4 eshared Step 3: ClSBeSCl
Step 4:
Calculation of formal charges shows that
for Be, FC 2 (2 0) 0 and for Cl, FC 7 (1 6) 0
In BeCl2, the chlorine atoms achieve the argon configuration, [Ar], and the beryllium atom has a share of only four electrons. Compounds such as BeCl2, in which the central atom shares fewer than 8 e, are sometimes referred to as electron deficient compounds. This “deficiency” refers only to satisfying the octet rule for the central atom. The term does not imply that there are fewer electrons than there are protons in the nuclei, as in the case of a cation, because the molecule is neutral.
A Lewis formula can be written for BeCl2that does satisfy the octet rule (see structure shown in the margin). Let us evaluate the formal charges for that formula:
for Be, FC 2 (4 0) 2 and for Cl, FC 7 (2 4) 1 We have said that the most favorable structure for a molecule is one in which the formal charge on each atom is zero, if possible. In case some atoms did have nonzero formal charges, we would expect that the more electronegative atoms (Cl) would be the ones with lowest formal charge. Thus, we prefer the Lewis structure shown in Example 7-5 over the one in the margin.
One might expect a similar situation for compounds of the other IIA metals, Mg, Ca, Sr, Ba, and Ra. These elements, however, have lower ionization energies and larger radii than Be, so they usually form ions by losing two electrons.
E
XAMPLE 7-6 Limitations of the Octet RuleWrite the Lewis formula for boron trichloride, BCl3, a covalent compound. Plan
This covalent compound of boron is an example of limitation type B. As we follow the steps in writing the Lewis formula, we use six electrons as the number needed by boron in step 2. Steps 3 and 4 should show only three pairs of electrons for boron.
Solution
Cl Step 1: The skeleton is Cl B Cl
Be Cl
Cl or Cl Be Cl
S
ee the Saunders InteractiveGeneral Chemistry CD-ROM,
Screen 9.7, Electron-Deficient Compounds.
see limitation type B g
Step 2: N 3 8 (for Cl) 1 6 (for B) 30 eneeded
Step 3: A 3 7 (for Cl) 1 3 (for B) 24 eavailable
Step 3: S N A 30 e 24 e 6 eshared Cl
h Step 3: ClSBSCl
Step 4:
Each chlorine atom achieves the Ne configuration. The boron (central) atom acquires a share of only six valence shell electrons. Calculation of formal charges shows that
for B, FC 3 (3 0) 0 and for Cl, FC 7 (1 6) 0 You should now work Exercise 54.
E
XAMPLE 7-7 Limitations of the Octet RuleWrite the Lewis formula for phosphorus pentafluoride, PF5, a covalent compound. Plan
We apply the usual stepwise procedure to write the Lewis formula. In PF5, all five F atoms are bonded to P. This requires the sharing of a minimum of 10 e, so this is an example of limi-tation type D. We therefore add the extra step 2a, and increase S from the calculated value of 8 eto 10 e.
Solution
Step 1: The skeleton is
Step 2: N 5 8 (for F) 1 8 (for P) 48 eneeded
Step 3: A 5 7 (for F) 1 5 (for P) 40 eavailable
Step 3: S N A 8 eshared
Step 2: Five F atoms are bonded to P. This requires the sharing of a minimum of 10 e. But only 8 ehave been calculated. This is therefore an example of limitation type D.
Step 2a: Increase S from 8 eto 10 e, the number required to bond five F atoms to one P atom. The number of electrons available, 40, does not change.
Step 3: F F F F F P B Cl Cl or Cl Cl B Cl Cl
7-7 Limitations of the Octet Rule for Lewis Formulas 293
F F F F F P
Step 4:
When the octets of the five F atoms have been satisfied, all 40 of the available electrons have been added. The phosphorus (central) atom has a share of ten electrons.
Calculation of formal charges shows that
for P, FC 5 (5 0) 0 and for F, FC 7 (1 6) 0
When an atom has a share of more than eight electrons, as does P in PF5, we say that it exhibits an expanded valence shell. The electronic basis of the octet rule is that one s and three p orbitals in the valence shell of an atom can accommodate a maximum of eight electrons. The valence shell of phosphorus has n 3, so it also has 3d orbitals available that can be involved in bonding. It is for this reason that phosphorus (and many other representative elements of Period 3 and beyond) can exhibit an expanded valence shell. By contrast, elements in the second row of the periodic table can never exceed eight elec-trons in their valence shells, because each atom has only one s and three p orbitals in that shell. Thus, we understand why PF5can exist but NF5cannot.
E
XAMPLE 7-8 Limitations of the Octet RuleWrite the Lewis formula for sulfur tetrafluoride, SF4. Plan
We apply the usual stepwise procedure. The calculation of S N A in step 2 shows only 6 e shared, but a minimum of 8 e are required to bond four F atoms to the central S atom. Limitation type D applies, and we proceed accordingly.
Solution
F F
Step 1: The skeleton is S
F F
Step 2: N 1 8 (S atom) 4 8 (F atoms) 40 eneeded
Step 3: A 1 6 (S atom) 4 7 (F atoms) 34 eavailable
Step 3: S N A 40 34 6 eshared. Four F atoms are bonded to the central S. This requires a minimum of 8 e, but only 6 ehave been calculated in step 2. This is therefore an example of limitation type D.
Step 2a: We increase S from 6 eto 8 e. Step 3: Step 4: F F F F S F F F F S or F F F F F P F F F F F P
This is sometimes referred to as
hypervalence.
